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JUNE 12345 6 7 8 9101112 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

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INDEX OF CURVE AND REDUCTION TABLES Table Table

I-SLOPE STAKE II-STADIA CORRECTION AND HORIZONTAL DISTANCES

Table III-TRIGONOMETRIC FORMULAE Table

IV-NATURAL TRIGONOMETRICAL FUNCTIONS CURVE FORMULAE

Table

V-TANGENTS AND EXTERNALS TO A 10 CURVE USEFUL RELATIONS

Table

VI-INCHES TO DECIMALS OF A FOOT

Table VII-MINUTES IN DECIMALS OF A DEGREE Table VIH-MIDDLE ORDINATES OF RAILS Table

IX-SHORT RADIUS CURVES

Table

X-RODS IN FEET, IOTHS AND 100THS OF FEET

Table XI-LINKS IN FEET, IOTHS AND 100THS OF FEET

TABLE I. SLOPE STAKE 435

DISTANCES FROM SIDE STAKES FOR CROSS-SECTIONING ROADWAY OF ANYWIDTH.SIDESLOPES 1Y 2 TO 1.

SIDE ISTAKE

SLOPE STAKE

SIDE ISTAKE

I C. L.

24.3

-

SLOPE STAKE

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-'10.7

I

16.05

3.6

. Distance out from Side or Shoulder Stake.

0

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.2

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1.4

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.8

.9

0.80 0.45 0.60 0.75 0.90 1.05 1.20 1.35 1 80 1.95 2.10 2.25 2.40 2.55 2.70 2.85 8.80 345 3.60 3 75 3.90 4.05 4.20 4 35 4.50 4.80 4.95 510 52.5 540 5.55 5.70 6.00 6.80 6.45 6.60 6 75 6.90 7.05 7.20 7 50 7.80 7.95 8.10 8.25 8.40 8.55 8.70 8.85 900 9.30 9.45 9.60 9.75 9.90 10.05 10.20 10.35 10.50 10.80 10.95 11.10 11.25 11.40 11.55 11 70 11.85 12.00 12.8012.45 12.60 12.75 12.90 13.05 13.20 13.35 13 50 13.65 133.95 14.10 14.25 14.40 14 55 14.70 15.00 15 15 15 80 15 45 15.60 15.75 15.90 16.05 16.20 16 35 16 50 16 65 16 80 16.95 17 10 17.25 17.40 17.55 17.70 17.85 18 00 18 15 S18.30 18 45 18.60 18 75 18.90 19.05 19.20 19 85 1950O19 6.5 109.80 19.95 20.10 20.252040 20.55 20.70 20.85 21.00 21 15 21.3021.45 21 60 21.75 21.90 22 05 2220 22 50 2265 S22 80 2295 23.10 28.25 23.40 23.55 23.70 23.85 24.00 2415 324 30 2445 24.6024.75 2490 25 05 25.20 25.50 2565 25.8025 95 26.10 2625 2640 26.5526.7026.85 27.00 27 15 27.3027 45 27.6027.75 27.90 28.05 2820 28 50 00 2865 2880 28.9529.10 29.25 29.40 29.55 29.7028.35 30 00 30 15 30. 0 30.45 30.60 30.75 30.90 81.05 31.20 31357 31 65 31.80 31.95 32 10 32 25 32.40 32.5532 70 82 85 31 50 33 15 33 30 33 45 33.60 33 75 33.90 34.05 34.2034.35 33 00 34 50 3465 34.80 34.95 35.10 85 25 35 40 35.5535.70 35 85 86.00 86 15 36.80 36 45 36.60 36.75 36.90 37.05 37.20 37.35 87.50 37.65 37 80 37.95 38.10 38.2538.40 38.55 38.70 38.85 39 00 39 15 39.8039 45 3960 39.75 39.90 40.05 40.2040.35 40 50 40 65 40 80 40.95 41.10 41.2541 40 41.55 41.70 41.85 42 00 42 15 42.3042.45 42.60 42 75 42.90 43.05 43.2048.35 43 50 4365 43.8043 95 44.10 4425 4440 44.5544.70 44 85 45 00 45 15 45.30 4545 45.60 45.75 45.90 46.054620 48.35 46.50 46.65 46.80 46 95 47.1047.25 47.40 47.55 47.70 47.85 48 00 48.15 48.30 4845 48.60 48 75 48.90 49.05 49 20 49.35 49.50 49 65 49.80 49.95 50.1050.25 50.4050.55 50.70 50.85 51 00 51.15 51.30 51.45 51.60 51.75 51.90 52.05 52.20 52.85 52 50 52.65 52.80 52.95 53.10 53.2553.40 53.55 583.70 53.85 54 00 64.15 54.30 54 45 54.60 54.75 54.90 55.05 55.2055.35 55 50 5565 55.8055.95 56.10 56.2556.40 56.55 56.70 56.85 57.00 57.15 57.3057 45 57.60 57 75 57.90 58.05 58.20 58 35 58.65 5880 58.9559.10 59 25 59.40 5955 59.70 59.8 60.15 60 30 60 45 6060 60.75 6090 61.05 6120 i61.3 598 5850 000

,

TABLE II. STADIA CORRECTION AND HORIZONTAL DISTANCES STADIA REDUCTIONS FOR READING 100 Horizontal Correction

Vertical Angle

2°--00'

30-00' 4°--00' 5°-00' 6°--00'

7°--00' 8°--00' 9°-00'

100-00, 10°-30'

110-00, 11°-30' 12°-00' 12°-30' 13°-00'

13°-30' 14°-00' 14°-30' 15°-00' 15°-30'

16°-00' 16°-30' 17°-00' 17°-30'

18-00' Chains to Feet 1 2 3 4 5 6 7 8 9 10

....... 66 ..........

132 ..........

198 ..........

264 .......... 330 ..........

396 ..........

462 ..........

528 ..........

594 ..........

660

Difference in Elevation

Horizontal Correction

Vertical Angle

Difference in Elevation

3.5 5.3 7.0 8.7 10.4

18°-30' 19°-00' 19°-30' 20°-00' 20°-30'

10.1 10.6 11.2 11.7 12.3

30.1 30.8 31.5 32.1 32.8

12.1 13.8 15.5 17.10 17.9

21 °-00' 210-30' 22°-00' 22°-30' 23°-00'

12.8 13.4 14.0 14.7 15.3

33.5 34.1 34.7 35.4 36.0

18.7 19.5 20.3 21.1 21.9

23°-30' 24°-00' 24° -30' 25-00' 25°-30'

15.9 16.5 17.2 17.9 18.6

36.6 37.2 37.7 38.3 39.0

22.7 23.4 24.2 25.0 25.8

26°-00' 26°-30' 27°-00' 27°-30' 28°-00'

19.2 19.9 20.6 21.3 22.0

39.4 39.9 40.5 41.0 42.0

26.5 27.2 28.0 28.7 29.4

280-30' 290-00' 290-30'

22.8 23.5 24.3 25.0

41.9 42.4 42.9 43.3

30Q00'

Feet to Chains 100 ....

1.515

200 ....

300 ....

3.030 4.545

400 ....

500 ....

6.060 7.575

.... .... .... .... ....

9.090 10.606 12.121 13.636 15.151

600 700 800 900 1,000

TABLE III. TRIGONOMETRIC FORMULAE B A

A

b

B

B

a

a

Ab

C A

a

C

Right Triangle Oblique Triangles Solution of Right Triangles a b a b e 0 For Angle A. sin= a ,cos= ,tan = a, cot -= ,sec = ,cosec = Given Required a , a. b A, B , tan A = = cotB,c = a = a 1 + = cos B, b= v'(c+a)(o-a)=

a,

A, B, b

sin A =

A, a

B, b, a

B = 90°-A, b = a cotA, c=

asin sin

B=90*-A, a = b tan A,

A.

A, b

B, a, c

A, c Given A, B, a

B = 90 0 -A, a = e sin A, b= ecos A, Solution of Oblique Triangles Required a sin B b, C, b sin A = 180-(A + B), a

= co

A, a, b

B, e,

b sin A sin B= b sin A a

a, b, O

A. B, c

A+B=180--C, tan

cos

A.

B, a, b

A, B,

a

8= a+

)(A-B)=(a-

a+ b+c

Area

8=a

A,

Area

area =

A, B, C,a Area

area =

,

b

, area =

b)tan )(A--B a

++b

bc)(-c

,sin JA=

s -a )(%-C 8 ,C=180*-(A+B)

sin B=.

4, b, c

a sin a si A

_sin O = 180°-(A + B), a= a sin A

a sin C sin A , b, c

1-

,

(s-b)(s--c)

sin A

a2 sin B sin C 2 sin 2 sin A

REDUCTION TO HORIZONTAL Horizontal distance -=Slope distance multiplied by the Vert. angle-5 10'. From Table. IV. cos 5 10i .9959.

Horizontal distance - 319.4 991 = 318.09 ft.

Horizontal distance also - Slope distance minus slope distance times l1-cosine of vertical angle). With the cosine of the vertical angle. Thus: slope distance =319.4 ft. °

boo

Horizontal distance

same figures as in the preceding example, the following result is obtained. Cosine 50 10= .950. -. 9959=.0041.

319.4X.0041=1.31. S19.4-1.31=318.09 ft.

When the rise is known, the horizontal distance is approximately:-the slope distance less the square of the rise divided by twice the slope distance. Thus: rase=14 ft.. slope distane-=302.6 ft. Horizontal distance=302.6- 14 14 =302.6-.32 30228 ft.

2 x 302.6

TABLE IV. NATURAL TRIGONOMETRICAL FUNCTIONS Angle

Sin

Tan.

Angle

Sin.

Ton.

Sec.

Cosec. Cotg.

Cosin.

1.0001 1.0001

O0 343.8 171.9 114.6 85.94 68.76

1.

1. .99998 .99996 .99993 .99989

1.0098 1.0102 1.0107 1.0111 1.0115 1.0120

7.185 7.040 6.900 6.766 6.636 6.512

.99027 .98986 .98944 .98902 .98858 .98814

1.0002 1.0002 1.0003 1.0003 1.0004 1.0005

57.30 49.11 42.98 38.20 34.38 31.26

.99985 99979 .99973 .99966 .99958 .99949

1.0125 1.0129 1 0134 1.0139 1.0144 1.0149

6.394 6.277 6.166 6.059 5.955 5.855

.98769 .98723 .98676 .98629 .98580 .98531

1.0006 1.0007 1 0008 1.0010

28.65 2645 24.56 22.93 21.49 20.23

.99939 .99929 .99917 .99905 .99892 .99878

1.0154 1.0160 1.0165 1.0170 1.0176 1.0181

5.759 5.665 5.575 5.488 5.403 5.320

.98481 .98430 .98378 .98325 .98272 .98218

1.0015 1.0017 1.0019 10020 1.0022

19.11 18.10 17.20 16 38 15.64 14.96

.99863 .99847 .99831 .99813 .99795 .99776

1.0187 1.0193 1.0199 1.0205 1 0211 1.0217

5.241 5.164 5.089 5.016 4.945 4.877

.98163 .98107 .98050 .97992 .97934 .97875

1.0024 1.0027 1.0029 1.0031 1.0033 1.0036

14.34 13.76 13.23 12.75 12.29 11.87

.99756 .99736 .99714 .99692 .99668 .99644

1.0223 1.0230 1.0236 1.0243 1.0249 1.0256

4.810 4.745 4.682 4.620 4.502

.97815 .97754 .97692 .97630 .97566 .97502

1.0038 1.0041 1.0043 1.0046 1.0049 1.0052

11.47 11.10 10.76 10.43 10.13 9.839

.99619 .99594 .99567 .99540 .99511 .99482

1.0263 1.0270 1.0277 1.0284 1.0291 1.0299

4.445 4.390 4.336 4.284 4.232 4.182

.97437 .97371 .97304 .97237 .97169 .97100

1.0055 1.0058 1.0061 1.0065 1.0068 1 0072

9.567 9.309 9.065 8.834 8.614 8.405

.99452 .99421 .99390 .99357 .99324 .99290

1.0306 1.0314 1.0321 1.0329 1.0337 1.0345

4.133 4.086 4.039 3.994 3.949 3.906

.97030 .96959 .96887 .96815 .96742 .96667

1.0075 1.0079 1.0082 1.0086 1.0090 1.0094

8.206 8.016 7.834 7661 7.496 7.337

.99255 .99219 .99182 .99144 .99106 .99067

1.0353 1 .0361 1.0369 1.0377 1.0386 1.0394

3.864 3.822 3.782 3.742 3.703 3.665

.96593 .96517 .96440 .96363 .96285 .96206

Cosec.

Sec.

1.0012 1.0014

Cotg.

Cosin.

Cosec.

1.0011

Cosin

Cotg.

Sec.

Cosec.

Sec.

Tan.

Sin. Angle

Cosin. Cotg.

4.560

Tan.

Sin.

Angle

TABLE IV CONTD. NATURAL TRIGONOMETRICAL FUNCTIONS Sec.

Cosec.

Cotg.

Cosin.

.96126 .96046 .95964 .95882 .95799 .95715

1.0946 1.0961 1.0975 1.0989 1.1004 1.1019

2.459 2.443 2.427 2.411 2.396 2.381

2.246 2.229 2.211 2.194 2.177 2.161

.91355 .91236 .91116 .90996 .90875 .90753

3.420 3.388 3.357 3.326 3.295 3.265

.95630 .95545 .95459 .95372 .95284 .95195

1.1034 1.1049 1.1064 1.1079 1.1095 1.1110

12.366 2.351 2.337 2.323 2.309 2.295

2.145 2.128 2.112 2.097 2.081 2.066

.90631 .90507 .90383 .90259 .90133 .90007

1.0525 1.0535 1.0545 1.0555 1.0566

3.236 3.207 3.179 3.152 3.124 3.098

.95106 .95015 .949241 .94832 .94740 .94646

1.1126 1.1142 1.1158 1.1174 1.1190 1.1207

2.281 2.268 2.254 2.241 2.228 2.215

2.050 2.035 2.020 2.006 1.991 1.977

.89879 .89752 .89623 .89493 .89363 .89232

19 .3256 .3443 1.0576 10 .32831.347611.0587 .3508 1.0598 .3541 1.0608 .3574 1.0619 .3607 1.0631

3.072 3.046 3.020 2.996 2.971 2.947

2.904 2.877 2.850 2.824 2.798 2.773

.94552 .94457 .94361 .94264 .94167 .94068

1.1223 1.1240 1.1257 1.1274 1.1291' 1.1308

2.203 2.190 2.178 2.166 2.154 2.142

1.963 1.949 1.935 1.921 1.907 1.894

.89101 .88968 .88835 .88701 .88566 .88431

.3640 .3673 .3706 .3739 .3772 .3805

1.0642 1.0653 1.0665 1.0676 1.0688 1.0700

2.924 2.900 2.878 2.856 2.833 2.811

2.747 2.723 2.699 2.675 2.651 2.628

.93969 .93869 .93769 .93667 .93565 .93462

1.1326 1.1343 1.1361 1.1379 1.1397 1.1415

2.130 2.119 2.107 2.096 2.085 2.073

1.881 1.868 1.855 1.842 1.829 1.816

.88295 .88158 .88020 .87882 .87743 .87603

.3839 .3872 .3906 .3939 .3973 .4006

1.0711 2.790 2.605 .93358 1.0723 2.769 2.583 .93253 1.0736 2.749 2.560 .93148 1.0748 2.729 2.539 .93042 1.0760 2.709 2.517 .92935 1.0773 2.689 2.496 .92827

1.1434 1.1452 1.1471 1.1490 1.1509 1.1528

2.063 2.052 2.041 2.031 2.020 2.010

1.804 1.792 1.780 1.767 1.756 1.744

.87462 .87321 .87178 .87036 .86892 .86748

.4040 .4074 .4108 .4142 .4176 .4210

1.0785 1.0798 1.0811 1.0824 1.0837 1.0850

2.670 2.650 2.632 2.613 2.595 2.577

2.475 2.455 2.434 2.414 2.394 2.375

.92718 .92609 .92499 .92388 .92276 .92164

1.1547 2.000 1.732 .86603 1.1566 1.990 1.720 .86457 1.1586 1.980 1.709 .86310 1.1606 1.970 1.698 .86163 1.1626 1.961 1.686 .86015 1.1646 1.951 1.675 .85866

.4245 .4279 .4314 .4348 .4383 .4417

1.0864 1.0877 1.0891 1.0904 1.0918 1.0932

2.559 2.542 2.525 2.508 2.491 2.475

2.356 2.337 2.318 2.300 2.282 2.264

.92050 .91936 .91822 .91706 91590 91472

1.1666 1.1687 1.1707 1.1728 1.1749 1.1770

1.924 1.932 1.923 1.914 1.905 1.896

1.664 1.653 1.643 1.632 1.621 1.611

.85717 85567 85416 85264 85112 84959

Cotg.

Cosec.

Sec.

Tan.

Sin.

Cosec.

Sec.

Ton.

Sin.

Angle

Sin.

Cosin.

Tn.

Sec.

Cosec.

.2867 .2899 .2931 .2962 .2994 .3026

1.0403 1.0412 1.0423 1.0429 1.0438 1.0448

3.628 3.592 3.556 3.521 3.487 3.453

.3057 .3089 .3121 .3153 .3185 .3217

1.0457 1.0466 1.0476 1.0485 1.0495 1.0505

.3249 .3281 .3314 .3346 .3378 .3411

1.0515

Cotg.

Angle

Cosin.

[ngle

Sin.

Cosin.

Tan.

Cotg.

Angle

TABLE IV CONTD. NATURAL TRIGONOMETRICAL, FUNCTIONS Angle Sin.

Cosin.

Tan.

Cotg.

Sec.

Cosec.

Cotg.

Cosin.

Angle

Sin.

Ton

Sec.

Cosec.

Cotg.

Cosin.

1.1792 1.887 1.1813 1.878 1.1835 1.870 1.1857 1.861 1.1879 1.853 1.1901 1.844

.84805 .84650 .84495 .84339 .84182 .84025

1.2868 1.2898 1.2929 1.2959 1.2991 1.3022

1.589 1.583 1.578 1.572 1.567 1.561

.77715 .77531 .77347 .77162 .76977 .76791

1.1924 1.1946 1.1969 1.1992 1.2015 1.2039

1.836 1.828 1.820 1.812 1.804 1.796

.83867 .83708 .83549 .83389 .83228 .83066

1.3054 1.3086 1.3118 1.3151 1.3184 1.3217

1.556 1.550 1.545 1.540 1.535 1.529

.76604 .76417 .76229 .76041 .75851 .75661

1.2062 1.2086 1.2110 1.2134 1.2158 1.2183

1.788 1.781 1.773 1.766 1.758 1.751

.82904 .82741 .82577 .82413 .82248 .82082

1.3251 1.3284 1.3318 1.3352 1.3386 1.3421

1.524 1.519 1.514 1.509 1.504 1.499

.75471 .75280 .75088 .74896 .74703 .74509

1.2208 1.2233 1.2258 1.2283 1.2309 1.2335

1.743 1.736 1.729 1.722 1.715 1.708

.81915 .81748 .81580 .81412 .81242 .81072

1.3456 1.3492 1.3527 1.3563 1.3600 1.3636

1.494 1.490 1.485 1.480 1.476 1.471

.74314 .74120 .73924 .73728 .73531 .73333

1.2361 1.2387 1.2413 1.2440 1.2466 1.2494

1.701 1.695 1.688 1.681 1.675 1.668

.80902 .80730 .80558 .80386 .80212 .80038

1.3673 1.3711 1 .3748 1.3786 1.3824 1.3863

1.466 1.462 1.457 1.453 1.448 1.444

.73135 .72937 .72737 .72537 .72337 .72136

1.2521 1.2549 1.2577 1.2605 1.2633 1.2661

1.662 1.655 1.649 1.643 1.636 1.630

.79864 .79688 .79512 .79335 .79158 .78980

1.3902 1.3941 1.3980 1.4020 1.4061 1.4101'

1.440 1.435 1.431 1.427 1.422 1.418

.71934 .71732 .71529 .71325 .71121 .70916

1.2690 1.2719 1.2748 1.2778 1.2808 1.2838

1.624 1.618 1.612 1.606 1.601 1.595

.78801 .78622 .78442 .78261 .78079 .77897

1.414

1.414

.70711

Cosec.

Sec.

Tan.

Sin. Angle

Cosin. Cotg.

Cosec.

Sec.

Tan.

Sin.

Angle

CURVE FORMULAE

CURVE TABLE Table of Tangent and External to a 10 Curve

A Angle of Intersection I

S

I

i

o

To find Tangent and External for curve of any other degree, divide by degree of curve and add correction found in column of corrections.

Degree of curve with a given I may be found by dividing tangent, (or external), opposite I by given tangent, (or external).

The distance from a point on the tangent to the curve is very nearly the square of the tangent length divided by twice the radius.

CURVE FORMULAS Radius:

R =

50 . sm % D

Length of Curve: L = 100 D also L =.0174533 X A X R Degree of Curve: D = 100 Tangent:

T

= R tan

1 A

LC -= 2R sin A Long Cord: Middle Ordinate: M = R (1-Cos External :

E = T tan

%

A

A)

TABLE V. TANGENTS AND EXTERNALS TO A 10 CURVE

7

E

110

50.00 58.34 66.67 75.01 83.34 91.68

.218 .297 .388 .491 .606 .733

10' 20' 30' 40' 50'

100.01 108.35 116.68 125.02 133.36 141.70

.873 1.024 1.188 1.364 1.552 1.752

10' 20' 30' 40' 50'

150.04 158.38 166.72 175.06 183.40 191.74

1.964 10°C. 2.188 T 2.425 .06 2.674 2.934 E 3.207 .003

10' 20' 30' 40' 50'

200.08 208.43 216.77 225.12 233.47 241.81

3.492 3.790 4.099 4.421 4.755 5.100

30

40

250.16 10' 258.51 20' 266.86 30' 275.21 40' 283.57 50' 291.92

60

10' 20' 30' 40.

5,0' 70

10' 20' 30' 40' 50'

5.459 5.829 6.211 6.606 7.013 7.432

l

-

10' 20' 30' 40' 50' 20

50

T

10 20' 30 40 50'

T T

20' 30' 40' 50' °

14

10' 20' 30' 40' 50'

150C.

T .09 E .004

300.28 7.863.

308.64 8.307 316.99 8.762 ° 325.35 9.230 333.71 9.710 20 C. T 342.08 10.202 .13 350.44 10.707 E 358.81 11.224 367.17 11.753 .006 375.54 12.294 383.91 12.847 392.28 13.413

652.81 37.070 661.25 38.031 669.70 39.006 678.15 39.993 686.60 40.992 695.06 42.004 703.51 43.029 711.97 44.066 720.44 45.116 728.90 46.178 737.37 47.253 745.85 48.341

754.32 49.441 10' 762.80 50.554 20' 771.29 51.679 30' 779.77 52.818 40' 788.26 53.969 50' 796.75 55.132

°

805.25 10' 813.75 20' 822.25 30' 830.76 40' 839.27 50' 847.78

16

°

856.30 10' 864.82 20' 873.35 30' 881.88 40' 890.41 50' 898.95

17

T 1061.9 10' 1070.6 20' 1079.2 30' 1087 8 40' 1096.4 50' 1105.1

226

10' 20' 30' 40' 50'

1165.7 10' 1174.4 20' 1183.1 30' 1191.8 40' 1200.5 50' 1209.2

23

T .13 E .011

°

56.309.

57.498 58.699 59.914 ° 61.141 20 C. T 62.381 .26 63.634 E 64.900 .022 66.178 67.470 68.774 70.091

90

400.66 10' 409.03 20' 417.41 30' 425.79 40' 434.17 50' 442.55

13.991 14.582 15.184 25°C. T 15.799 16.426 .16 17.065 E 450.93 17.717 .007 10' 459.32 18.381 20' 467.71 19.058 30' 476.10 19.746 40' 484.49 20.447 50' 492.88 21.161 °

100

10' 20' 30' 40' 50'

501.28 509.68 518.08 526.48 534.89 543.29

907.49 10' 916.03 20' 924.58 30' 933.13 40' 941.69 50' 950.25

18

°

19

10' 20' 30' 40' 50'

71.421 ° 72.764 74.119 25 C. T 75.488 76.869 .32 78.264 E .028 958.81 79.671 967.38 81.092 975.96 82.525 984.53 83.972 993.12 85.431 1001.7 86.904 1010.3 1018.9 1027.5 1036.1 1044.7 1053.3

88.389 89.888 91.399 92.924 94.462 96.013

1322.8 10' 1331.6 20' 1340.4 30' 1349.2 40' 1358.0 50' 1366.8

150.71.

152.69 154.69 156.70 158.72 20 C. 160.76 T .39 162.81 164.86 E 166.95 .051 169.04 171.15 173.27

°

1375.6 10' 1384.4 20' 1393.2 30' 1402.0 40' 1410.9 50' 1419.7

27

°

1481.8 1490.7 1499.6 1508.5 1517.4 1526.3

1535.3 10' 1544.2 20' 1553.1 30' 1562.1 40' 1571.0 50' 1580.0

202.12 30 C. T 204.44 206.77 .59 209.12 E 211.48 213.86 .078

10' 20' 30' 40' 50' °

29

10' 20' 30' 40' 50'

30'C. T .39 E .034

1428.6 1437.4 1446.3 1455.1 1464.0 1472.9

15° C.

175.41 177.55 179.72 25' C. T 181.89 184.08 .49 186.29 E 188.51 .065 190.74 192.99 195.25.

197.53 199.82

28

°

21.887 30 C. 20 22.624 10' T 23.375 .19 20' 24.138 30' E 24.913 40' 25.700 .008 50' T a = 1E T = R tan /2I

139.11 T 141.01 .29 142.93 E 144.85 146.79 .038 148.75

10' 20' 30' 40' 50' °

117.38 10 C. 119.12 T 120.87 122.63 .19 124.41 E 126.20 .025

1270.2 1279.0 1287.7 1296.5 1305.3 1314.0

°

25

26

97.577 99.155 5o C. 100.75 102.35 T 103.97 .10 105.60 E 107.24 .013 108.90 110.57 112.25 113.95.

115.66

128.00 129.82 131.65 133.50 135.35 137.23

10' 20' 30' 40' 50'

15° C.

T .19 E .017

=30*

1217.9 1226.6 1235.3 1244.0 1252.8 1261.5

24

°

80

1113.7 1122.4 1131.0 1139.7 1148.4 1157.0

°

100 C.

E

°

21

31.561 32,447 33.347 34.259 35.183 36.120

°

15

1.20 I

551.70 26.500 560.11 27.313 568.53 28.137 576.95 28.974 585.36 29.824 593.79 30.686

1210 602.21 10' 610.64 20' 619.07 30' 627.50 40' 635.93 50' 644.37 1310

E E

°

30

xe E = R exsec 1/zI

°

TABLE V CONTD. TANGENTS AND EXTERNALS TO A 10 CURVE I 310

10' 20' 30' 40' 50'

°

32

10' 20' 30' 40' 50' °

33

10' 20' 30' 40' 50' °

34

10' 20' 30' 40' 50' 35

36

°

10' 20' 30' 40' 50' °

10' 20' 30' 40' 50' °

37

10' 20' 30' 40' 50' °

38

10' 20' 30' 40' 50' °

39

10' 20' 30' 40' 50'

T

1=40 °

E

1589.0 1598.0 1606.9 1615.9 1624.9 1633.9

216.3 218.7 221.1 223.5 226.0 228.4

1643.0 1652.0 1661.0 1670.0 1679.1 1688.1

230.9 233.4 235.9 238.4 241.0 243.5

1697.2 1706.3 1715.3 1724.4 1733.5 1742.6

246.1 100C. 248.7 T 251.3 .26 253.9 E 256.5 259.1 .046

1751.7 1760.8 1770.0 1779.1 1788.2 1797.4

261.8 264.5 267.2 269.9 272.6 275.3

1806.6 1815.7 1824.9 1834.1 1843.3 1852.5

278.1 280.8 283.6 286.4 289.2 292.0

1861.7 1870.9 1880.1 1889.4 1898.6 1907.9

294.9 297.7 300.6 303.5 ° 306.4 309.3 20 C. T 312.2 .53 315.2 E 318.1 321.1 .093 324.1 327.1

1917.1 1926.4 1935.7 1945.0 1954.3 1963.6 1972.9 1982.2 1991.5 2000.9 2010.2 2019.6

I

E

2142.2 2151.7 2161.2 2170.8 2180.3 2189.9

387.4 390.7 394.1 397.4 400.8 404.2

51

2199.4 2209.0 2218.6 2228.1 2237.7 2247.3

407.6 411.1 414.5 418.0 421.4 425.0

52

10' 20' 30' 40' 50'

2257.0 2266.6 2276.2 2285.9 2295.6 2305.2

428.5 10° C. 432.0 T 435.6 439.2 .34 442.8 E 446.4 .075

53

10' 20' 30' 40' 50'

2314.9 2324.6 2334.3 2344.1 2353.8 2363.5

10' 20' 30' 40' 50'

2373.3 2383.1 2392.8 2402.6 2412.4 2422.3

450.0 453.6.

457.3 461.0 464.6 468.4 15°C. T 472.1 .51 475.8 479.6 E 483.4 .116 487.2 491.0

54

10' 20' 30' 40' 50'

10' 20' 30' 40' 50'

2432.1 2441.9 2451.8 2461.7 2471.5 2481.4

10' 20' 30' 40' 50'

2491.3 2501.2 2511.2 2521.1 2531.1 2541.0

41 0

5o C. T .13 E .023

10' 20' 30' 40' 50' °

42

10' 20' 30' 40' 50'

I °

10' 20' 30' 40' 50' °

10' 20' 30' 40' 50' °

°

43

10' 20' 30' 40' 50'

°

15°C. T .40 E .070

2029.0 2038.4 2047.8 2057.2 2066.6 2076.0

330.2 333.2 250 C. 336.3 T 339.3 342.4 .67 345.5 E 348.6 .117 351.8 354.9358.1 361.3 364.5

2085.4 2094.9 2104.3 2113.8 2123.3 2132.7

367.7 30 C. T 371.0 374.2 .80 377.5 E 380.8 384.1 .141

°

45

°

46

°

47

E

1=60*

618.4 622.8 627.2 631.7 636.2 640.7

2794.5 2804.9 2815.2 2825.6 2835.9 2846.3

645.2 649.7 654.3 658.8 663.4 668.0

2856.7 2867.1 2877.5 2888.0 2898.4 2908.9

672.7 10°C. 677.3 T 682.0 686.7 .42 E 691.4 696.1 .112

10' 20' 30' 40' 50'

2551.0 2561.0 2571.0 2581.0 2591.0 2601.1

°

49

10' 20' 30' 40' 50' °

50

10' 20' 30' 40' 50'

10' 20' 30' 40' 50'

2919.4 2929.9 2940.4 2951.0 2961.5 2972.1

700.9 705.7 710.5 715.3 720.1 725.0 150C. T 729.9 .63 734.8 739.7 E 744.6 .168 749.6 754.6

°

55

10' 20' 30' 40' 50' °

494.8 498.7 502.5 506.4 ° 510.3 20 C. 514.3 T .68 518.2 E 522.2 526.1 .151 530.1 534.2538.2

56

542.2 546.3 550.4 25° C. 554.5 T 558.6 .85 562.8 E 566.9 .189 571.1 575.3579.5 583.8 588.0

58

2982.7 2993.3 3003.9 3014.5 3025.2 3035.8

3110.9 3121.7 3132.6 3143.4 3154.2 3165.1

759.6 764.6 769.7 ° 774.7 20 C. 779.8 T 784.9 .84 790.1 E 795.2 .225 800.4 805.6 810.9 816.1

10' 20' 30' 40' 50'

3176.0 3186.9 3197.8 3208.8 3219.7 3230.7

821.4 826.7 832.0 837.3 842.7 848.1

10' 20' 30' 40' 50'

3241.7 3252.7 3263.7 3274.8 3285.8 3296.9

853.5 858.9 864.3 869.8 875.3 880.8

3308.0 3319.1 3330.3 3341.4 3352.6 3363.8

886.4 30 C. 892.0 T 897.5 1.27 903.2 E 908.8 914.5 .340

10' 20' 30' 40' 50' °

57

10' 20' 30' 40' 50'

3046.5 3057.2 3067.9 3078.7 3089.4 3100.2

°

°

48

1 /ar Rtan T= R tan 1/2 T=

T 2732.9 2743.1 2753.4 2763.7 2773.9 2784.2

°

44 ,

2611.2 2621.2 2631.3 2641.4 2651.5 2661.6

°

59

°

°

40°

I=50

°

T

2671.8 2681.9 2692.1 2702.3 2712.5 2722.7

° 592.3 30 C. 60 596.6 T 10' 600.9 1.02 20' 605.3 30' E 609.6 40' 614.0 .227 50' E = R exsec 1 E = R exsec 1/2I

°

25

C.

T 1.05 E .283

TABLE V CONTD. TANGENTS AND EXTERNALS TO A 1 I

T

E

I=70

3375.0 3386.3 3397.5 3408.8 3420.1 3431.4

920.2 925.9 931.6 937.3 943.1 948.9

3442.7 3454.1 3465.4 3476.8 3488.3 3499.7

954.8 960.6 966.5 972.4 978.3 984.3

3511.1 10' 3522.6 20' 3534.1 30' 3545.6 40' 3557.2 50' 3568.7

990.2 996.2 1002.3 1008.3 1014.4 1020.5

61 o 10' 20' 30' 40' 50' °

62

10' 20' 30' 40' 50' °

63

°

°

10° C. T .51 E .159

1063.9 1070.2 1076.6 1082.9 1089.3 1095.7

3720.9 3732.7 3744.6 3756.5 3768.5 3780.4

1102.2 1108.6 1115.1 1121.7 20* C. 1128.2 T 1134.8 1.02 1141.4 E 1148.0 1154.7 .321 1161.3 1168.1 1174.8

°

68

10' 20' 30' 40' 50' °

69

10' 20' 30' 40' 50' °

70

10' 20' 30' 40' 50'

3792.4 3804.4 3816.4 3828.4 3840.5 3852.6

1352.6 1360.1 1367.6 1375.2 1382.8 1390.4

4239.7 4252.6 4265.6 4278.5 4291.5 4304.6

1398.0 1405.7 1413.5 1421.2 1429.0 1436.8

4317.6 4330.7 4343.8 4356.9 4370.1 4383.3

1444.6 1452.5 1460.4 1468.4 1476.4 1484.4

4396.5 4409.8 4423.1 4436.4 4449.7 4463.1

1492.4 1500.5 1508.6 1516.7 1524.9 1533.1

4476.5 4489.9 4503.4 4516.9 4530.4 4544.0

1541.4 1549.7 1558.0 1566.3 1574.7 1583.1

10' 20' 30' 40' 50'

4557.6 4571.2 4584.8 4598.5 4612.2 4626.0

1591.6 1600.1 1608.6 1617.1 1625.7 1634.4

10' 20' 30' 40' 50'

4639.8 4653.6 4667.4 4681.3 4695.2 4709.2

1643.0 1651.7 1660.5 1669.2 1678.1 1686.9

10' 20' 30' 40' 50'

4723.2 4737.2 4751.2 4765.3 4779.4 4793.6

1695.8 1704.7 1713.7 1722.7 1731.7 1740.8

10' 20' 30' 40' 50'

4807.7 4822.0 4836.2 4850.5 4864.8 4879.2

1749.9 1759.0 1768.2 1777.4 1786.7 1796.0

°

73

10' 20' 30' 40' 50' 10' 20' 30' 40' 50'

150C.

T .76 E .240

3937.9 3950.2 3962.5 3974.8 3987.2 3999.5

1181.6 1188.4 1195.2 25° C. T 1202.0 1208.9 1.28 1215.8 E 1222.7 .403 1229.7 1236.7 1243.7 1250.8 1257.9

4011.9 4024.4 4036.8 4049.3 4061.8 4074.4

1265.0 30 C. T 1272.1 1279.3 1.54 1286.5 E 1293.6 1300.9 .485

3864.7 3876.8 3889.0 3901.2 3913.4 3925.6

4162.8 4175.6 4188.5, 4201.2 4214.0 4226.8

740

°

10' 20' 30' 40' 50'

+

10' 20' 30' 40' 50'

3650.2 3661.9 3673.7 3685.4 3697.2 3709.0

°

1308.2 1315.6 1322.9 1330.3 1337.7 1345.1

°

650 10' 20' 30' 40' 50'

67

4086.9 4099.5 4112.1 4124.8 4137.4 4150.1

o

72

1026.6 1032.8 1039.0 1045.2 1051.4 1057.7

10' 20' 30' 40' 50'

I= 80

10' 20' 30' 40' 50'

3580.3 3591.9 3603.5 3615.1 3626.8 3638.5

66

E

I

71

10' 20' 30' 40' 50'

64

I

°

75

10' 20' 30' 40' 50'

1176° 10' 20' 30' 40' 50' °

77

780

°

79

°

°

80

T = R tan 1/21

°

T

10 C. T .61 E .220

10 20' 30' 40' 50'

4893.6 4908.0 4922.5 4937.0 4951.5 4966.1

1805.3 1814.7 1824.1 1833.6 1843.1 1852.6

10' 20' 30' 40' 50'

4980.7 4995.4 5010.0 5024.8 5039.5 5054.3

1862.2 1871.8 1881.5 1891.2 1900.9 1910.7

10' 20' 30' 40' 50'

5069.2 5084.0 5099.0 5113.9 5128.9 5143.9

1920.5 1930.4 1940.3 1950.3 1960.2 1970.3

10' 20' 30' 40' 50'

5159.0 5174.1 5189.3 5204.4 5219.7 5234.9

1980.4 1990.5 2000.6 2010.8 2021.1 2031.4

10' 20' 30' 40' 50'

5250.3 5265.6 5281.0 5296.4 5311.9 5327.4

2041.7 2052.1 2062.5 2073.0 2083.5 2094.1

5343.0 5358.6 5374.2 5389.9 5405.6 5421.4

2104.7 2115.3 2126.0 2136.7 2147.5 2158.4

5437.2 5453.1 5469.0 5484.9 5500.9 5517.0

2169.2 2180.2 2191.1 2202.2 2213.2 2224.3

5533.1 5549.2 5565.4 5581.6 5597.8 5614.2

2235.5 2246.7 2258.0 2269.3 2280.6 2292.0

5630.5 5646.9 5663.4 5679.9 5696.4 5713.0

2303.5 2315.0 2326.6 2338.2 2349.8 2361.5

5729.7 5746.3 5763.1 5779.9 5796.7 5813.6

2373.3 2385.1 2397.0 2408.9 2420.9 2432.9

81

820

°

83

°

°

85

°

86

10' 20' 30' 40' 50'

°

20 C. T 1.22 E .445

°

87

10' 20' 30' 40' 50' °

88 250 C. T 1.53 E .558

10' 20' 30' 40' 50' °

89

10' 20' 30' 40' 50' 30 C. T 1.84 E .671

E

T

84

15°C. T .91 E .332

CURVE

I °

5 C. T .30 E .110

°

°

90

10' 20' 30' 40' 50'

E = R exsec 1/21

I=90

°

10 C. T .72 E .299

15 C. T 1.09 E .450

°

20 C. T 1.45 E .603

°

25 C. T 1.83 E .756

300 C. T 2.20 E .910

TABLE V CONTD. TANGENTS AND EXTERNALS TO A 10 CURVE I 910

10' 20' 30' 40' 50' 920

10' 20' 30' 40' 50' 930

10' 20' 30' 40' 50' 940

10' 20' 30' 40' 50' 950

10' 20' 30' 40' 50' 960

10' 20' 30' 40' 50' 970

10' 20' 30' 40' 50' 980

°

6950.6 6971.3 6992.0 7012.7 7033.6 7054.5

3278.1 3294.1 3310.1 3326.1 3342.3 3358.5

7075.5 7096.6 7117.8 7139.0 7160.3 7181.7

3374.9 3391.2 3407.7 3424.3 3440.9 3457.6

7203.2 7224.7 7246.3 7268.0 7289.8 7311.7 7333.6 7355.6 7377.8 7399.9 7422.2 7444.6

3474.4 10 C. 3491.3 T 3508.2 3525.2 .103 3542.4 E 3559.6 .536 3576.8 3594.2 3611.7 3629.2 3646.8 3664.5 15° C.

6252.8 6271.1 6289.4 6307.9 6326.3 6344.8

2594.0 10°C. 1030 2606.8 10' T 2619.7 20' 2632.6 .86 30' 2645.5 40' E 2658.5 .401 50' 1040 2671.6 2684.7 10' 2697.9 20' 2711.2 30' 40' 2724.5 2737.9 15° C, 50' T 1050 2751.3 1.30 10' 2764.8 2778.3 20' E 2792.0 30' 2805.6 .604 40' 2819.4 50'

7467.0 7489.6 7512.2 7534.9 7557.7 7580.5

3682.3 3700.2 3718.2 3736.2 3754.4 3772.6

6363.4 6382.1 6400.8 6419.5 6438.4 6457.3

2833.2 2847.0 2861.0 2875.0 2889.0 2903.1

7603.5 7626.6 7649.7 7672.9 7696.3 7719.7

3791.0 3809.4 3827.9 ° 3846.5 3865.2 20 C. T 3884.0 2.08 3902.9 E 3921.9 3940.9 1.08 3960.1 3979.43998.7

1160

4018.2 4037.8 4057.4 25' C. T 4077.2 4097.1 2.61 4117.0 E 4137.1 1.36 4157.3 4177.5 4197.9 4218.4 4239.0

1180

5830.5 5847.5 5864.6 5881.7 5898.8 5916.0

2444.9 2457.1 2469.3 2481.5 2493.8 2506.1

1010

5933.2 5950.5 5967.9 5985.3 6002.7 6020.2

2518.5 2531.0 2543.5 2556.0 2568.6 2581.3

1020

6037.8 6055.4 6073.1 6090.8 6108.6 6126.4 6144.3 6162.2 6180.2 6198.3 6216.4 6234.6

10' 20' 30' 40' 50' 10' 20' 30' 40' 50'

1060

°

10' 20' 30' 40' 50'

20 C T 1.74 1070 6476.2 2917.3 E 10' 6495.2 2931.6 .809 20' 6514.3 2945.9 6533.4 2960.3 30' 40' 6552.6 2974.7.

6571.9 2989.2 50' 6591.2 6610.6 6630.1 6649.6 6669.2 6688.8

3003.8 3018.4 3033.1 3047.9 3062.8 3077.7

1080

7743.2 7766.8 7790.5 7814.3 7838.1 7862.1 7886.2 7910.4 7934.6 7959.0 7983.5 8008.0 8032.7 8057.4 8082.3 8107.3 8132.3 8157.5

°

1000

10' 20' 30' 40' 50'

6828.3 6848.5 6868.8 6889.2 6909.6 6930.1

30 C 1100 T 10' 20' 2.62 30' 40' 50' 1.22 ta /z/-LE R-tan IT = =R

3184.1 3199.6 3215.1 3230.8 3246.5 3262.3

-I;110

I

E

I

E

° 10' 25 C 20' T 30' 40' 2.18 50' E 990 1.02 1090 6708.6 3092.7 10' 10' 6728.4 3107.7 20' 6748.2 3122.9.

20' 30' 6768.1 3138.1 30' 40' 40' 6788.1 3153.3 50' 6808.2 3168.7 50'

10' 20' 30' 40' 50'

°

T

1=100

T

+ 5"C.

T .51 E .268

10' 20' 30' 40' 50' 1120

10' 20' 30' 40' 50' °

T 1.56 E .806

°

8182.8 8208.2 8233.7 8259.3 8285.0 8310.8

1110

1130

10' 20' 30' 40' 50' 1140

10' 20' 30' 40' 50' 1150

10' 20' 30' 40' 50' 10' 20' 30' 40' 50' 1170

10' 20' 30' 40' 50' 10' 20' 30' 40' 50' 1190

10' 20' 30' 40' 50'

T

E

8336.7 8362.7 8388.9 8415.1 8441.5 8468.0

4386.1 4407.6 4429.2 4450.9 4472.7 4494.6

8494.6 8521.3 8548.1 8575.0 8602.1 8629.3

4516.6 4538.8 4561.1 4583.4 4606.0 4628.6

8656.6 8684.0 8711.5 8739.2 8767.0 8794.9

4651.3 4674.2 4697.2 4720.3 4743.6 4766.9

8822.9 8851.0 8879.3 8907.7 8936.3 8965.0

4790.4 4814.1 4837.8 4861.7 4885.7 4909.9

8993.8 9022.7 9051.7 9080.9 9110.3 9139.8

4934.1 4958.6 4983.1 5007.8 5032.6 5057.6

9169.4 9199.1 9229.0 9259.0 9289.2 9319.5

5082.7 5107.9 5133.3 5158.8 5184.5 5210.3

9349.9 9380.5 9411.3 9442.2 9473.2 9504.4

5236.2 5262.3 5288.6 5315.0 5341.5 5368.2

9535.7 9567.2 9598.9 9630.7 9662.6 9694.7

5395.1 5422.1 5449.2 5476.5 5504.0 5531.7

9727.0 9759.4 9792.0 9824.8 9857.7 9890.8

5559.4 5587.4 5615.5 5643.8 5672.3 5700.9

4259.7 30 C. 1200 9924.0 5729.7 4280.5 T 10' 9957.5 5758.6 4301.4 3.14 20' 9991.0 5787.7 4322.4 30' L0025.0 5817.0 E 4343.6 40' L0059.0 5846.5 4364.8 1.63 50' L0093.0 5876.1 exe E = R exsec I/2.

I=120

°

5oC. T .62 E .360

10°C.

T 1.25 E .721

15° C.

T 1.93 E 1.09

°

20 C. T 2.52 E 1.46

25' C. T 3.16 E 1.83

°

30 C. T 3.81 E 2.20

USEFUL RELATIONS Lineal feet X.00019 = miles Lineal yards X.0006 = miles Square inches X.007 = square feet Square feet X.111 = square yards Square yards X.0002067 = acres Acres x 4840 = square yards Cubic inches X.00058 = cubic feet X.03704 = cubic yards Cubic feet = yards x.22 Links Links x.66 = feet Feet x 1.5 = links -360 째 = 21600' = 1296000" 째 Radius = are of 57.2957790 째 Arc of 1 (radius = 1) = .017453292 Arc of 1' (radius = 1) = .000290888 Arc of 1" (radius = 1) = .000004848 Curvature of Earth's surface = about 0.7 feet in 1 mile Curvature in feet = 0.667 (Dist. in miles)' Difference between arc and chord length, 0.05 feet in 11% miles Probable error of a single observation = 0.6754 Error in chaining of 0.01 feet in 100 feet: Due to1. Length of tape error of 0.01 feet 2. Alignment. One end 1.4 feet out of line 3. Sag of tape at center of 0.61 feet.

4. Temperature difference of 15 째 5. Difference of pull of 15 lbs.

SQUARE MEASURE 144 sq. inches = 1 sq. ft.

9 sq. ft. = 1 sq. yard 30 4 sq. yds. = 1 sq. rd.

40 sq. rds. = 1 rood.

4 roods = 1 acre 640 acres - 1 sq. mile.

SURVEYORS' MEASURE 7.92 inches = 1 link.

25 links = 1 rod.

4 rds. --- 1 chain.

10 sq. chains or 160 sq. rods = 1 acre.

640 acres = 1 sq. mile.

36 sq. miles (6 miles sq.) = 1 township.

-

1

TABLE VI. INCHES TO DECIMALS OF A FOOT

I.

0

1

2

0 1-32 1-16 3-32 1-8 5-32 3-16 7-32

Foot .0026 .0052 .0078 .0104 .0130 .0156 .0182

.0833 .0859 .0885 .0911 .0938 .0964 .0990 .1016

.1667 .1693 .1719 .1745 .1771 .1797 .1823 .1849

1-4 9-32 5-16 11-32 3-8 13-32 7-16 15-32 1-2 17-32 9-16 19-32 5-8 21-32 11-16 23-32 3 25-32 13-16 27- 2 7-8 29-32 15-16 31-32

.0208 .1042 .0234 .1068 .0260 .1094 .0286 .1120 .0313 .1146 .0339 .1172 .0365 .1198 .0391 .1224 .0417 .1250 .0443 .1276 .0469 .1302 .0495 .1328 .0521 .1354 .0547 .1380 .0573.1406 .0599 1432 .0625 .1458 .0651 .1484 .0677 .1510 .0703.1536 .0729 .1563 .0755.1589 .0781 .1615 .0807 .1641 0

1

.00833 .01667 .02500 .03333 .04167 .05000 .05833 .06667 .07500 .08333 .09167 .10000 .10833 .11667 .12500 .13333 .14167 .15000 .15833 .16667

4

.2500 .3333 .2526 .3359 .2552 .3385 .2578 .3411 .2604 .3438 .2630.3464 .2656 .3490 .2682 .3516

.1875 .2708 .1901 .2734 .1927 .2760 .1953.2786 .1979 .2813 .2005 .2839 .2031 .2865 .2057 .2891 .2083 .2917 .2109 .2943 .2135 .2969 .2161 .2995 .2188 .3021 .2214 .3047 .2240 .3073 2266 .3099 .2292 .3125 .2318 .3151 .2344.3177 .2370 .3203 .2396 .329 .2422 .3255 .2448 .3281 .2474 .3307 38

2

TABLE VII. 0' 30" 1 00 30 2 00 30 3 00 30 4 00 30 5 00 30 6 00 30 7 00 30 8 00 30 9 00 30 10 00

3

5

.4167 .4193 .4219 .4245 .4271 .4297 .4323 .4349

6

7

5

9

.5000 .5833 .6667 .5026 .5859.6693 .5052.5885 .6719 .5078 .5911 .6745 .5104 .5938 .6771 .5130.5964 .6797 .5156 .5990 .6823 .5182 .6016 .6849

.3542 .4375 .5208 .6042 .3568 .4401 .5234 .6068 .3594 .4427 .5260 .6094 .3620 .4453 .5286 .6120 .3646 .4479 .5313 .6146 .3672 .4505 .5339 .6172 .3698 .4531 .5365 .6198 .3724 .4557 .5391 .6224 .3750 .4583 .5417 .6250 .3776 .4609 .5443 .6276 .3802 .4635 .5469 .6302 .3828 .4661 .5495 .6328 .3854 .4688 .5521 .6354 .3880! .4714 .5547 .6380 .39061.4740.573.6406 .3932 .4766 .5599 .6432 .3958 .4792 .5625 .6458 .3984 .4818 .5651 .6484 .4010 .4844 .5677.6510 .4036 .4870.5703.6536 .4063 .4896.5729 .6563 .4089 .4922.5755 .6589 .4115 .4948 .5781 .6615 .4141 .4974 .5807 .6641 4

8

6

7

10

11

.7500 .8333 .9167 .7526 .8359 .9193 .7552.8385 .9219 .7578 .8411 .9245 .7604 .8438 .9271 .7630 .8464 .9297 .7656 .8490 .9323 .7682 .8516 .9349

In.

0 1-32 1-16 3-32 1-8 5-32 3-16 7-32

.5875 .7708 .8542 .9375 1-4 .6901 .7734 .8568 .9401 9-32 .6927 .7760 .8594 .9427 6-16 .6953 .7786 .8620 .945311-32 .6979 .7813 .8646 .9479 3-8 .7005 .7839 .8672 .9505 13-32 .7031 .7865 .8698 .9531 7-16 .7057 .7891 .8724 .9557 15-32 .7083 .7917 .8750 .9583 1-2 .7109 .7943 .8776 .9609 17-32 .7135 .7969 .8802 .9635 9-16 .7161 .7995 .8828 .9661 19-32 .7188 .8021 .8854 .9688 5-8 .7214 .8047 .8880 .9714 21-32 .7240.8073.8906.9740 11-16 .7266 .8099 .8932 .9766 23-32 .7292 .8125 .8958 .9792 8-4 .7318 .8151 .8984 .981825-32 .7344.8177.9010.9844 13-16 .7370 .8203 .9036 .9870 27-32 .9896 7-8 .899063 .7422 .8255 .9089 .9922 29-32 .7448 .8281 .9115 .9948 15-16 .7474 .8307 .9141 .9974 31-32 8

9

10

11

MINUTES IN DECIMALS OF A DEGREE

10' 30" .17500 11 00 .18333 30 .19167 12 00 .20000 30 .20833 13 00 .21667 30 .22500 14 00 .23333 30 .24167 15 00 .25000 30 .25833 16 00 .26667 30 .27500 17 00 .28333 30 .29167 18 00 .30000 30 .30833 19 00 .31667 30 .32500 20 00 .33333

20' 30" .34167 21 00 .35000 30 .35833 22 00 .36667 30 .37500 23 00 .38333 30 .39167 24 00 .40000 30 .40833 25 00 .41667 30 .42500 26 00 .43333 30 .44167 27 00 .45000 30 .45833 28 00 .46667 30 .47500 29 00 .48333 30 .49167 30 00 .500000

30' 30" .50833 31 00 .51667 30 .52500 32 00 .53333 30 .54167 33 00 .55000 30 .55833 34 00 .56667 30 .57500 35 00 .58333 30 .59167 36 00 .60000 30 .60833 37 00 .61667 30 .62500 38 00 .63333 30 .64167 39 00 .65000 30 .65833 40 00 .66667

40' 30" .67500 50' 41 00 .68333 51 30 .69167 42 00 .70000 52 30 .70833 43 00 .71667 53 30 .72500 44 00 .73333 54 30 .74167 45 00 .75000 55 30 .75833 46 00 .76667 56 30 .77500 47 00 .78333 57 30 .79167 48 00 .80000 58 30 .80833 49 00 .81667 59 30 .82500 50 00 .83333 60

30" 00 30 00 30 00 30 00 30 00 30 00 30 00 30 00 30 00 30 00

.84167 .85000 .85833 .86667 .87500 .88333 .89167 .90000 .90833 .91667 .92500 .93333 .94167 .95000 .95833 .96667 .97500 .98333 .99167 1.00000

TABLE VIII. MIDDLE ORDINATES OF RAILS

Length of Rail (feet) C o0 0-20 0-40 1-0 1-20 1-40 2-0 2-20 2-40 3-0 3-20 3-40 4-0 4-20 4-40 5 6 7

R Feet 17189 8594 5730 4297 3438 2865 2456 2149 1910 1719 1563 1433 1323 1228 1146 955.3 819.0

30 28 26 24 22 20 Inch Inch Inch Inch Inch Inch

C o

.08 .16 .24 .31 .39 .47 .55 .63 .71 .78 .86 .94 1.02 1.10 1.18 1.41 1.65

8 9 10 11 12 13 14 15 16 17 18 19 20 22 24 26

.07 .14 .20 .27 .34 .41 .48 .55 .62 .68 .75 .82 .89 .96 1.03 1.23 1.44

.06 .1 .18 .23 .29 .35 .41 .47 .53 .59 .65 .71 .77 .83 .89 1.06

.05 .10 .15 .20 .25. .30 .35 .40 .45 .50 .55 .60 .65 .70 .75 .90 1.05

.04 .08 .13 .17 21 .25 .29 .33 .38 .42 .46 .50 .55 .59 .63 .76 .89

.03 .07 .10 .13 .17 .20 .23 .27 .31 .35 .38 .42 .45 .48 .52 .62 .73

R Feet

30 28 26 24 22 20 Inch inch Inch Inch Inch Inch

716.8 1.88 1.64 1.42 1.20 1.01 .84 637.3 2.12 1.84 1.60 1.35 1.14 .94 573.7 2.36 2.05 1.78 1.50 1.27 1.04 521.7 2.59 2.26 1.95 1.65 1.39 1.15 478.3 3.83 2.47 2.15 1.81 1.54 1.26 441.7 3.05 2.66 2.30 1.96 1.66 1.36 410.3 3.30 2.87 2.48 2.10 1.78 1.46 383.1 3.54 3.08 2.68 2.26 1.91 1.57 359.3 3.76 3.28 2.832.40 2.04 1.67 338.3 4.00 3.483.02 2.572.161.78 319.6 4.21 3.67 3.18 2.70 2.28 1.87 302.9 4.45 3.89 3.36 2.862.41 1.98 287.9 4.70 4.09 3.65 3.00 2.4 2.09 262.0 5.16 4.44 3.84 3.302.80 2.29 240.5 5.64 4.92 4.20 3.59 3.04 2.50 222.3 6.07 5.29 4.58 3.88 3.29 2.70

TABLE IX. SHORT RADIUS CURVES Badlus Feet

Chord Feet

Central Angle

Deflection Angle

Deflection for 1 Foot

35 45 50 60 75 100 120 150 190 200 225 240 250

10 10 15 15 15 20 20 20 25 25 25 25 25

16-26 12-46 17-16 14-22 11-30 11-30 9-34 7-39 7-32 7-10 6-25 5-58 5-44

8-13 6-23 8-38 7-11 5-45 5-45 4-47 3-49 3-46 3-35 3-12 2-59 2-52

49.3 38.3 34.5 28.8 23.0 17.3 14.3 11.5 9.15 8.6 7.7 7.2 6.9

275

25

5-12

2-36

6.2

288 300 350 376 400 410

50 50 50 50 50 50

9-58 9-32 8-12 7-40 7-10 7-00

4-59 4-46 4-06 3-50 3-35 3-30

6.0 5.7 4.9 4.6 4.3 4.2

To find length of curve divide angle from P. C. to P. T. by central angle of chord, and multiply by length of chord.

TABLE X. RODS IN FET, IOTHS AND lOOTIIS OF FEET

Feet

0

Feet

346.50 363.00 379.50 396.00 412.50 429.00 445.50 462.00 478.50 495.00 511.50 528.00 544.50 561.00 577.50 594.00 610.50 627.00 643.50 660.00

41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

676.50 693.00 709.50 726.00 742.50 759.00 775.50 792.00 808.50 825.00 841.50 858.00 874.50 891.00 907.50 924.00 940.50 957.00 973.50 990.00

Feet

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

16.50 33.00 49.50 66.00 82.50 99.00 115.50 132.00 148.50 165.00 181.50 198.00 214.50 231.00 247.50 264.00 280.50 297.00 313.50 330.00

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Feet

Feet

61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

1006.50 1023.00 1039.50 1056.00 1072.50 1089.00 1105.50 1122.00 1138.50 1155.00 1171.50 1188.00 1204.50 1221.00 1237.50 1254.00 1270.50 1287.00 1303.50 1320.00

81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

1336.50 1353.00 1369.50 1386.00 1402.50 1419.00 1435.50 1452.00 1468.50 1485.00 1501.50 1518.00.

1534.50 1551.00 1567.50 1584.00 1600.50 1617.00 1633.50 1650.00

TABLE XI. LINKS IN FEET, IOTHS AND 100THS OF FEET SFeet

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

0.66 1.32 1.98 2.64 3.30 3.96 4.62 5.28 5.94 6.60 7.26 7.92 8.58 9.24 9.90 10.56 11.22

.

Feet

18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

11.88 12.54 13.20 13.86 14.52 15.18 15.84 16.50 17.16 17.82 18.48 19.14 19.80 L0.46 21.12 21.78 22.44

Feet

35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

23.10 23.76 24.42 25.08 25.74 26.40 27.06 27.72 28.38 29.04 29.70 30.36 31.02 31.68 32.34 33.00 33.66

.

Feet

52 34.32 53 34.98 54 35.64 55 36.30 56 36.96 57 37.62 58 38.28 59 38.94 60 39.60 61 40.26 62 40.92 63 41.58 64 42.24 65 42.90 66 43.56 67 44.22 68 44.88

69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85

Feet

.5 a

Feet

45.54 46.20 46.86 47.52 48.18 48.84 49.50 50.16 50.82 51.48 52.14 52.80 53.46 54.12 54.78 55.44 56.10

86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102

56.76 57.42 58.08 58.74 59.40 60.06 60.72 61.38 62.04 62.70 63.36 64.02 64.68 65.34 66.00 66.66 67.32

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